Multiloop calculations in p-adic string theory and Bruhat-Tits trees
type: Item
instance of: scholarly article
title: Multiloop calculations in p-adic string theory and Bruhat-Tits trees
zbMATH Open document ID: 0685.22005
DOI: 10.1007/BF01228348
published in: Communications in Mathematical Physics
publication date: 1989-01-01T00:00:00Z
review text: The approach to p-adic string theory proposed by the third author [ibid. 123, No.3, 463-483 (1989; Zbl 0676.22006)] is further developed. In [loc. cit.] the p-adic analog of the interior of the open string world sheet has been proposed to be a Bruhat-Tits tree T; moreover, a simple local action on T (of gaussian type) has been constructed which reproduces the correct p-adic amplitudes. In the present paper the multiloop generalization of the above results is considered. The B-T tree is viewed as a p-adic zero genus surface. The p-adic surfaces of higher genera are obtained by factorizing this tree by some Schottky group. This gives a graph with cycles. By considering the reduced graph, i.e. the graph obtained by retaining only the cycles, one can introduce the p-adic counterpart of the Jacobian and other relevant notions. To produce the string amplitudes out of a local action one has to solve the analog of Neumann boundary problem. The problem of finding the relevant Green functions is solved within path integral approach. Having this done the authors calculate the tachyon string amplitudes. Finally, some mathematical problems concerning the correct normalization and construction of the amplitudes for the emission of higher spin states are discussed.
Mathematics Subject Classification ID: 22E35
Mathematics Subject Classification ID: 81T08
Mathematics Subject Classification ID: 83E99
Mathematics Subject Classification ID: 30F10
Mathematics Subject Classification ID: 14H25
zbMATH DE Number: 4122247
zbMATH Keywords: p-adic string theory
zbMATH Keywords: open string world sheet
zbMATH Keywords: Bruhat-Tits tree
zbMATH Keywords: p-adic surfaces
zbMATH Keywords: Schottky group
zbMATH Keywords: string amplitudes
zbMATH Keywords: Green functions
zbMATH Keywords: path integral
zbMATH Keywords: tachyon string amplitudes
zbMATH Keywords: normalization
author: Leonid Chekhov
author: A. Mironov
author: A. Zabrodin
reviewed by: Paweł Maślanka
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01228348
OpenAlex ID: W2059785306
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description: scientific article; zbMATH DE number 4122247